Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
290 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17987554 | C3 | semidirect |
| 4. #17987553 | C3 | semidirect |
| 5. C27×#4296 | C3 | semidirect |
| 7. #13095344 | C9 | semidirect |
| 8. #13095343 | C9 | semidirect |
| 9. #13095342 | C9 | semidirect |
| 16. C3×#10587018 | C9 | semidirect |
| 17. C27×C19⋊C3 | C9 | semidirect |
| 18. C27×C19⋊C3 | C9 | semidirect |
| 19. C27×C19⋊C3 | C9 | semidirect |
| 23. C3×C19×C27 | C9 | semidirect |
| 71. C3×C27 | #4296 | semidirect |
| 97. C19 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| #17987589 | 3 |
| #17987554 | 3 |
| #17987553 | 3 |
| C27×#4296 | 3 |
| C3×C27×C19⋊C3 | 3 |
| #10624681 | 19 |